Certificate for #545 ⟨a, b, c | bb=aa, bc=a⟩

Back:⟨a, b, c | bb=aa, bc=a⟩

Completion settings:

[1] aa=bb

Axiom: bb=aa.

Flip LHS and RHS.

Referenced by [3].

[2] a=bc

Axiom: bc=a.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3].

[3] bcbc=bb

Overlap of [1] aa=bb with [2] a=bc:

aa a

Critical pair: bca=bb.

Reduce LHS:

[2]bc(a)
⇒ bcbc

Defines rule #1.

Referenced by [4].

[4] bbbc=bcbb

Overlap of [3] bcbc=bb with [3] bcbc=bb:

bc bc bcbc

Critical pair: bcbb=bbbc.

Flip LHS and RHS.

Defines rule #2.